THE CTMC METHOD AS PART OF THE STUDY OF CLASSICAL CHAOTIC HAMILTONIAN-SYSTEMS

Stability features of dynamical systems are frequently attributed to t he implications of the Kolmogoroff-Arnold-Moser (KAM) theorem. However , application of this theorem requires compact phase-space regions. Th is is not the case in the hyperbolic Coulomb three-body problem encoun tered in most of the classical trajectory Monte Carlo (CTMC) applicati ons. Therefore, the satisfactory results of the clue method in a wide energy region or its robustness with respect to perturbations cannot b e interpreted in this way. We propose here a justification of the abov e properties based on the character of the space of initial conditions corresponding to the trajectory classes resulting in excitation, ioni zation and charge transfer. Numerical experiments are in progress in o rder to confirm that the algebraic dimension of the boundaries separat ing the three sets of trajectories is, indeed, fractal, so that the sy stem could be at least partly classified as a chaotic dynamical system . The stability properties of the CTMC method can then be inferred str aightforwardly, since chaotic dynamical systems are structurally stabl e.